Theresa May was under pressure to say how plans to give the NHS an extra £384 million a week will be paid for as she delivers a key note speech on health funding.

The Prime Minister’s claim that a “Brexit dividend” will help fund the 3.4% increase in spending was widely attacked as unrealistic – even by some Conservatives.

And Mrs May has so far refused to be drawn on whether stealth taxes, such as delaying rises in income tax thresholds, and higher borrowing will fund the planned raising of the health budget by £20 billion a year in real terms by 2024.

Tory chairwoman of the Commons Health Committee Sarah Wollaston branded talk of a Brexit bonanza “tosh” as she said voters were being treated like fools.

Director of the Institute for Fiscal Studies, Paul Johnson, also said the so-called windfall from EU withdrawal would not materialise when the UK stopped paying more than £9 billion a year to Brussels due to the “divorce bill” of some £39 billion, and other economic factors.

Labour, which said it would match the Tory funding proposals if in power, called on Mrs May to set out details of how her plan would be paid for.

Mrs May is using her speech in London to say the NHS has a special place in British life, stating: “I will never forget visiting the Royal Manchester Children’s Hospital in the aftermath of the Manchester Arena attack. There, in the face of the very worst that humanity can do, I witnessed first-hand, the very best.

“Doctors and nurses working 24-hour shifts to treat the injured. Surgeons who were off-shift, dropping everything to come in and perform life-saving operations.

“Paramedics who had risked their own lives to get others to safety. In every instance, I was struck not only by the medical expertise of the staff, but the compassion with which people were treated. This is our National Health Service.”

The PM is also recalling her own reliance on the NHS for help when she was diagnosed with Type 1 diabetes, saying: “I would not be doing the job I am doing today without that support.”

Of the increased investment, Mrs May is set to say: “The NHS will be growing significantly faster than the economy as a whole, reflecting the fact that the NHS is this Government’s number one spending priority.

“This must be a plan that ensures every penny is well spent. It must be a plan that tackles waste, reduces bureaucracy and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care.”

The PM has set aside an additional £1.25 billion each year on top of the settlement to cover specific pensions pressure in order to focus the extra investment on frontline care, a Downing Street spokesman said.

Shadow chancellor John McDonnell told BBC Radio 4’s Today programme: “We need to have confidence in what’s being said. It’s all well and good making an announcement like this and trying to hit the headlines, but to be credible you have to say where the money’s coming from. We certainly haven’t seen that.

“The speculation about where it’s coming from – particularly the ‘Brexit dividend’ – is just not credible, as far as many commentators are saying. And we still haven’t addressed social care.”